Divide. Write the quotient in lowest terms. $3\dfrac{3}{10} \div 1\dfrac47 = $
Explanation: First, let's rewrite $3\dfrac3{10}$ and $1\dfrac47$ as fractions: $3\dfrac{3}{10} \div 1\dfrac47 =\dfrac{33}{10} \div \dfrac{11}{7}$ [How do we write a mixed number as a fraction?] Dividing by a fraction is the same as multiplying by the reciprocal of the fraction. The reciprocal of $\dfrac{11}7$ is $\dfrac7{11}$. Now, we can rewrite our expression as a multiplication problem: $\dfrac{33}{10} \div \dfrac{11}7=\dfrac{33}{10}\times\dfrac7{11}$ $=\dfrac{33\times 7}{10 \times 11}$ $=\dfrac{ \stackrel{3}{\cancel{33}} \times~ 7 }{ 10\times\underset{1}{\cancel{11}}} $ $=\dfrac{3\times 7}{10 \times 1}$ $=\dfrac{21}{10}$ We could also write this as $2\dfrac1{10}$.